WASHINGTON—The effort to overhaul the anti-sexual harassment rules governing lawmakers has stalled over disagreements about the conduct for which senators and members of the House can be held personally financially responsible, aides said.

In December, accusations of misconduct roiled Congress, culminating in the resignation or retirement of several lawmakers from both parties.

Amid a nationwide movement to curb harassment in businesses, media, Hollywood and politics, the House and Senate earlier this year passed legislation aimed at overhauling Congress’s sexual-harassment policies.

But the two bills have yet to be reconciled and sent to the president’s desk to become law.

House lawmakers say the Senate would water down their bill, while senators worry the House bill would leave them with too much financial exposure by leaving in place an overly broad definition of sexual harassment and discrimination.

Because lawmakers are amending an existing law on workplace conduct, they must pass legislation agreed on by both chambers.

“We’re not quite there yet,” said Rep. Gregg Harper, chairman of the House Administration Committee, which wrote that chamber’s sexual harassment-related legislation. Mr. Harper, a Mississippi Republican, didn’t say when he hoped the dispute would be resolved.

Senate Rules Committee Chairman Roy Blunt (R., Mo.), who sponsored the Senate’s sexual harassment bill, said he was having “productive, ongoing discussions with the House” and “will continue working to get sexual-harassment legislation to the president’s desk.”

The current law, known as the Congressional Accountability Act, bars discrimination based on race, color, religion, sex or national origin, but members aren’t personally responsible for settlements of cases reported to an internal congressional office that arbitrates them. Settlements are paid by taxpayers, from an account set up for that purpose.

In one instance, former Rep. Blake Farenthold of Texas used public funds to settle an accusation of misconduct brought by a former staffer. House Speaker Paul Ryan called on Mr. Farenthold to pay back the money, but he left Congress without doing so. Lawmakers want to ban the practice of using taxpayer funds to settle cases against lawmakers.

In the House bill, if a sexual harassment or discrimination case is brought against a member and settled, the member is on the hook for the monetary settlement.

The Senate bill narrows the definition of the conduct for which lawmakers could be financially responsible: unwelcome sexual advances or sexual harassment that interferes with work performance or creates a hostile working environment. Lawmakers would also be allowed an additional review before they are personally held financially responsible for the settlement.

The bills would also reform how complaints of misconduct are handled. The current process requires mediation and waiting periods that victims say are cumbersome. None of the cases brought to light last year were handled through the outlined process. Former Rep. Trent Franks (R., Ariz.) was asked to leave Congress by Mr. Ryan after allegations surfaced that Mr. Franks had pressured employees to be a surrogate parent for his child. Mr. Franks said he regretted that his behavior caused stress.

After sexual-harassment claims were brought to light, both chambers passed resolutions making sexual-harassment awareness training mandatory.

At least $600,000 in taxpayer funds has gone to settling workplace misconduct claims in the Senate over the past 20 years, according to the Senate Rules Committee. The House has paid $199,000 over the past 10 years to settle four claims of sexual harassment against lawmakers and Capitol Hill staff.